Linear Independence: Proving Dependency of {v1,v2,v3,v4}

[EV33]

Homework Statement

If the set {v1,v2,v3} of vectors in R^(m) is linearly dependent, then argue that the set {v1,v2,v3,v4} is also linearly dependent for every choice of v4 in R^(m).

Homework Equations

Definitions would be more relevant so...

Linearly Independent: If the only solution is the trivial solution

Linearly Dependent: If there are more solutions than he trivial solution.

The Attempt at a Solution

I started out by writing out three vectors that are a dependent set, and I noticed that no matter what I added for v4 there would still be that non trivial solution, therefore making it remain dependent.

Is that sound reasoning?

 

[tiny-tim]

Hi EV33!

(try using the X² and X₂ tags just above the Reply box )

I started out by writing out three vectors that are a dependent set, and I noticed that no matter what I added for v4 there would still be that non trivial solution, therefore making it remain dependent.

Is that sound reasoning?

If I'm guessing correctly what you mean, then yes that's sound.

But you should write it properly, starting "if v₁ v₂ and v₃ are dependent, then there exist …"

 

[EV33]

Thank you very much